Create custom physics for an object with python
Yes it is possible, there are 2 ways of doing this, but there are also 2 big drawbacks for both methods:


method 1: You can script your own modifier in c++, here is how to start. The drawback is you need to build your own Blender version yourself. Modifiers cannot be add with python or addons. If your modifier gets approved it can be added in the trunk (official release).
method 2: You can add your physics simulation code in the app handlers. This way your code gets executed for example every frame change. You can manipulate objects, change mesh etc. This will work from addon but the code will be very slow and you will unlikely get real-time fps.